1. Chapter 2: Data Abstraction 2.1 Specifying Data via Interfaces
Interface vs. Implementation
Interface: How the data “talks to” the outside world, a.k.a. client
Implementation: How the data is represented internally
Data types like this are said to be abstract.
Like Java...

2. public interface Message {
public void report(String msg); }
public class StdoutMessage implements Message {
public void report(String msg) {
System.out.println(msg); }

3. An Example from Scheme: Nonnegative Integers
Semantics:
“The representation of n”
(iszero? [n]) = #t n = 0
#f n ≠ 0
(succ [n]) = [n+1] (n ≥ 0)
(pred [n+1]) = [n] (n ≥ 0)

4. E.g., “Silly” Representation Items Representation l l l d l l ` l b @
(iszero? d) = #f
= #t
(succ b) = `

5. An Example from Scheme: Nonnegative Integers
Client: implementation-independent
(define plus
(lambda (x y)
(if (iszero? x) y
(succ (plus (pred x) y)))))

6. Nonnegative Integers: Unary implementation
[0] = ()
[n+1] = (cons #t [n])
(define zero '())
(define iszero? null?)
(define succ (lambda (n) (cons #t n)))
(define pred cdr)

7. Nonnegative Integers: Ordinary implementation
(define zero 0 )
(define iszero? zero?)
(define succ (lambda (n) (+ n 1)))
(define pred (lambda (n) (- n 1)))